On symplectic representations of normal j-algebras and their application to Xu's realizations of Siegel domains
On symplectic representations of normal j-algebras and their application to Xu's realizations of Siegel domains
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DOI：
10.1016/j.difgeo.2006.02.001
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发表时间：
2006-12
影响因子：
0.5
通讯作者：
H. Ishi
中科院分区：
文献类型：
--
作者：
H. Ishi
给出了给定正规j代数的内射正规辛表示的一个正则构造。另一方面，利用满足某些公理的矩阵的向量空间，将对应于任何正规辛表示的全纯映射的象描述为西格尔上半平面的子集。结合这些结果，我们自然得到了Xu的齐次Siegel域的实现[Y.C.]徐，齐次有界域的自同构群，数学学报。中国科学19 (1976)161-191；徐永昌，齐次有界域的同构性，数学学报。中国科学，20(1977)248-266。
We present a canonical construction of an injective normal symplectic representation of a given normal j-algebra. On the other hand, the image of the holomorphic map corresponding to any normal symplectic representation is described as a subset of the Siegel upper half plane by using vector spaces of matrices satisfying certain axioms. Combining these results, we naturally obtain Xu's realization of homogeneous Siegel domains [Y.C. Xu, Automorphism groups of homogeneous bounded domains, Acta Math. Sinica 19 (1976) 161–191; Y.C. Xu, On the isomorphism of homogeneous bounded domains, Acta Math. Sinica 20 (1977) 248–266].